Disentangling universality from shape in Platonic granular packings

Understanding how particle shape controls the macroscopic properties of granular materials is a longstanding challenge in soft matter physics. For polyhedral particles, flat facets introduce strong directional interactions crucial for both local order and global stability. However, how these interactions propagate across length scales to form disordered structures remains unclear, hindering a predictive statistical framework linking particle shape to packing statistics. Here, using magnetic resonance imaging, we reconstruct the disordered packings of granular particles of all five Platonic solids. We show that face-face contacts are binomially distributed, with a probability that encodes shape-specific geometric frustration and universally controls the size of face-face connected clusters. These clusters grow diffusively and exhibit random-walk statistics independent of particle shape or packing fraction, whereas local density fluctuations are governed by face-face contact number and global packing fraction. Our results bridge particle-scale geometry, mesoscale cluster statistics and global packing fraction, providing a unified basis for a statistical mechanical theory of non-equilibrium assemblies of disordered polyhedral packings.